//
//---------------------  1D  ---------------------
//
//
// Quick is not defined for 1D
//

//
//---------------------  3D  ---------------------
//
//       Staggered Mesh for w-vel and v-vel
//
//   0       1       2       3       4       5   
//
//5      >       >       >       >       > 
//       |       |       |       |       |              
//   ^---+---^---+---^---+---^---+---^---+---^  4       Mesh for scalar fields
//       |       |       |       |       | 
//4      >   o   >   o   >   o   >   o   >               5  x-x-+-x-+-x-+-x-x
//       |       |       |       |       |               4  x o | o | o | o x
//   ^---+---^---+---^---+---^---+---^---+---^  3           +---+---+---+---+
//       |       |       |       |       |               3  x o | o | o | o x
//3      >   o   >   o   >   o   >   o   >                  +---+---+---+---+
//       |       |       |       |       |               2  x o | o | o | o x
//   ^---+---^---+---^---+---^---+---^---+---^  2           +---+---+---+---+
//       |       |       |       |       |               1  x o | o | o | o x
//2      >   o   >   o   >   o   >   o   >               0  x-x-+-x-+-x-+-x-x
//       |       |       |       |       |                  
//   ^---+---^---+---^---+---^---+---^---+---^  1           0 1   2   3   4 5 
//       |       |       |       |       |                 
//1      >   o   >   o   >   o   >   o   >                 o central node
//       |       |       |       |       |                 x boundary node
//   ^---+---^---+---^---+---^---+---^---+---^  0          > w velocity 
//       |       |       |       |       |                 ^ v velocity
//0      >       >       >       >       >    
//       0       1       2       3       4             
//
//                                                  
//          Volumes for w-velocity
//
//   0       1       2       3       4       5
//
//5      >       >       >       >       > 
//       :       :       :       :       :              
//   ^...+---^---+---^---+---^---+---^---+...^  4       Mesh for scalar fields
//       |   |   :   |   :   |   :   |   | 
//4      >   o   >   o   >   o   >   o   >               5  x-x-+-x-+-x-+-x-x
//       |   |   :   |   :   |   :   |   |               4  x o | o | o | o x
//   ^...+---^---+---^---+---^---+---^---+...^  3           +---+---+---+---+
//       |   |   :   |   :   |   :   |   |               3  x o | o | o | o x
//3      >   o   >   o   >   o   >   o   >                  +---+---+---+---+
//       |   |   :   |   :   |   :   |   |               2  x o | o | o | o x
//   ^...+---^---+---^---+---^---+---^---+...^  2           +---+---+---+---+
//       |   |   :   |   :   |   :   |   |               1  x o | o | o | o x
//2      >   o   >   o   >   o   >   o   >               0  x-x-+-x-+-x-+-x-x
//       |   |   :   |   :   |   :   |   |                  
//   ^...+---^---+---^---+---^---+---^---+...^  1           0 1   2   3   4 5 
//       |   |   :   |   :   |   :   |   |                 
//1      >   o   >   o   >   o   >   o   >                 o central node
//       |   |   :   |   :   |   :   |   |                 x boundary node
//   ^...+---^---+---^---+---^---+---^---+...^  0          > w velocity 
//       :       :       :       :       :                 ^ v velocity
//0      >       >       >       >       >    
//
//       0       1       2       3       4              
//
//                       
//                  |           |           |           |
//                --^-----------^-----------^-----------^-- 
//                  |     :     |     :     |     :     |               
//                  |     :     | (i,j+1,k) |     :     |
//                  o     >     o    w_N    o     >     o   
//                  |     :     |     :     |     :     |
//                  |     :     |     :     |     :     |
//                --^---------- 3 -- v_n -- 4 ----------^--  4 = v(i+1, j  ,k)
//                  |     :     |     :     |     :     |    3 = v(i  , j  ,k)
//                  |     :     |     :     |     :     |    2 = v(i+1, j-1,k)
//                  o    w_B   w_b   w_P   w_f   w_F    o    1 = v(i  , j-1,k)
//                  | (i,j,k-1) |  (i,j,k)  | (i,j,k+1) |
//                  |     :     |     :     |     :     |
//                --^---------- 1 -- v_s -- 2 ----------^-- 
//                  |     :     |     :     |     :     |               
//                  |     :     |     :     |     :     |
//                  o     >     o    w_S    o     >     o   
//                  |     :     | (i,j-1,k) |     :     |
//                  |     :     |     :     |     :     |
//                --^-----------^-----------^-----------^--
//                  |           |           |           | 
//                   
//   w_b = ( w(i,j,k-1) + w(i,j,k) ) / 2     
//   w_f = ( w(i,j,k+1) + w(i,j,k) ) / 2
//   v_n = ( v(i,j,k) + v(i+1,j,k) ) / 2   
//              3           4
//   v_s = ( v(i,j-1,k) + v(i+1,j-1,k) ) / 2
//              1           2

//   u_e = ( u(i,j,k) + u(i,j+1,k) ) / 2
//   u_w = ( u(i-1,j,k) + u(i-1,j+1,k) ) / 2
// 

namespace Tuna {

template<class Tprec, int Dim>
inline bool Quick_ZHay<Tprec, Dim>::calcCoefficients3D () {
    prec_t dyz = dy * dz, dyz_dx = Gamma * dyz / dx;
    prec_t dxz = dx * dz, dxz_dy = Gamma * dxz / dy;
    prec_t dxy = dx * dy, dxy_dz = Gamma * dxy / dz;
    prec_t dxyz_dt = dx * dy * dz / dt;
    prec_t ce, cem, cep, cw, cwm, cwp, CE, CW;
    prec_t cn, cnm, cnp, cs, csm, csp, CN, CS;
    prec_t cf, cfm, cfp, cb, cbm, cbp, CF, CB;
    aE = 0.0; aW = 0.0; aN = 0.0; aS = 0.0; aF = 0.0; aB = 0.0; aP = 0.0; 
    sp = 0.0;
    
    for (int k = bk; k <= ek; ++k)
      for (int i =  bi; i <= ei; ++i)
	for (int j = bj; j <= ej; ++j)
	  {
	    CE = ce = ( u(i  ,j  ,k) + u(i  ,j+1,k  ) ) * 0.5 * dyz;
	    CW = cw = ( u(i-1,j  ,k) + u(i-1,j+1,k  ) ) * 0.5 * dyz;
	    CN = cn = ( v(i  ,j  ,k) + v(i+1,j  ,k  ) ) * 0.5 * dxz;
	    CS = cs = ( v(i  ,j-1,k) + v(i+1,j-1,k  ) ) * 0.5 * dxz;
	    CF = cf = ( w(i  ,j  ,k) + w(i  ,j  ,k+1) ) * 0.5 * dxy;
	    CB = cb = ( w(i  ,j  ,k) + w(i  ,j  ,k-1) ) * 0.5 * dxy;
	    cem = cep = 0.0;
	    cwm = cwp = 0.0;
	    cnm = cnp = 0.0;
	    csm = csp = 0.0;
	    cfm = cfp = 0.0;
	    cbm = cbp = 0.0;

	    // QUICK as presented in Hayase et al.
// ---- X
	    if ( ce > 0 ) { 
	      CE = 0;
	      if (i == bi) {
		cep = ce * (phi_0(i+1,j,k) - phi_0(i-1,j,k)) / 3.0;
	      } else {
		cep = ce * 0.125 * (-phi_0(i-1,j,k) - 2*phi_0(i,j,k) + 3*phi_0(i+1,j,k));
	      }
	    } else {
	      // The case i == ei is taken in to account in applyBoundaryConditions3D.
	      if (i == ei-1) {
		cem = ce * (phi_0(i+2,j,k) - phi_0(i,j,k)) / 3.0;
	      } else if (i < ei-1) {
		cem = ce * 0.125 * (-phi_0(i+2,j,k) - 2*phi_0(i+1,j,k) + 3*phi_0(i,j,k));
	      }
	    }
	    
	    if ( cw > 0 ) { 
	      // The case i == bi is taken in to account in applyBoundaryConditions3D.
	      if (i == bi+1) {
		cwp = cw * (phi_0(i,j,k) - phi_0(i-2,j,k)) / 3.0;
	      } else if (i > bi+1) {
		cwp = cw * 0.125 * (-phi_0(i-2,j,k) - 2*phi_0(i-1,j,k) + 3*phi_0(i,j,k));
	      }
	    } else {
	      CW = 0;
	      if (i == ei) {
		cwm = cw * (phi_0(i-1,j,k) - phi_0(i+1,j,k)) / 3.0;
	      } else {
		cwm = cw * 0.125 * (-phi_0(i+1,j,k) - 2*phi_0(i,j,k) + 3*phi_0(i-1,j,k));
	      }
	    }

// ---- Y
	    if ( cn > 0 ) { 
	      CN = 0;
	      if (j == bj) {
		cnp = cn * (phi_0(i,j+1,k) - phi_0(i,j-1,k)) / 3.0;
	      } else {
		cnp = cn * 0.125 * (-phi_0(i,j-1,k) - 2*phi_0(i,j,k) + 3*phi_0(i,j+1,k));
	      }
	    } else {
	      if (j == ej-1) {
		cnm = cn * (phi_0(i,j+2,k) - phi_0(i,j,k)) / 3.0;
	      } else if (i < ei-1) {
		cnm = cn * 0.125 * (-phi_0(i,j+2,k) - 2*phi_0(i,j+1,k) + 3*phi_0(i,j,k));
	      }
	    }
	    
	    if ( cs > 0 ) { 
	      if (j == bj+1) {
		csp = cs * (phi_0(i,j,k) - phi_0(i,j-2,k)) / 3.0;
	      } else if (j > bj+1) {
		csp = cs * 0.125 * (-phi_0(i,j-2,k) - 2*phi_0(i,j-1,k) + 3*phi_0(i,j,k));
	      }
	    } else {
	      CS = 0;
	      if (j == ej) {
		csm = cs * (phi_0(i,j-1,k) - phi_0(i,j+1,k)) / 3.0;
	      } else {
		csm = cs * 0.125 * (-phi_0(i,j+1,k) - 2*phi_0(i,j,k) + 3*phi_0(i,j-1,k));
	      }
	    }

// ---- Z
	    if ( cf > 0 ) { 
	      CF = 0;
	      cfp = cf * 0.125 * (-phi_0(i,j,k-1) - 2*phi_0(i,j,k) + 3*phi_0(i,j,k+1));
	    } else {
	      if (k == ek) {
		cfm = cf * 0.125 * (-5*phi_0(i,j,k+1) + 6*phi_0(i,j,k) - phi_0(i,j,k-1));
	      } else {
		cfm = cf * 0.125 * (-phi_0(i,j,k+2) - 2*phi_0(i,j,k+1) + 3*phi_0(i,j,k));
	      }
	    }
	    
	    if ( cb > 0 ) { 
	      if (k == bk) {
		cbp = cb * 0.125 * (-5*phi_0(i,j,k-1) + 6*phi_0(i,j,k) - phi_0(i,j,k+1));
	      } else {
		cbp = cb * 0.125 * (-phi_0(i,j,k-2) - 2*phi_0(i,j,k-1) + 3*phi_0(i,j,k));
	      }
	    } else {
	      CB = 0;
	      cbm = cb * 0.125 * (-phi_0(i,j,k+1) - 2*phi_0(i,j,k) + 3*phi_0(i,k,k-1));
	    }
	    
	    aE (i,j,k) = dyz_dx - CE;
	    aW (i,j,k) = dyz_dx + CW;
	    aN (i,j,k) = dxz_dy - CN;
	    aS (i,j,k) = dxz_dy + CS;
	    aF (i,j,k) = dxy_dz - CF;
	    aB (i,j,k) = dxy_dz + CB;
	    aP (i,j,k) = aE (i,j,k) + aW (i,j,k) + aN (i,j,k) + aS (i,j,k) 
	      + aF (i,j,k) + aB (i,j,k) + dxyz_dt
	      + (ce - cw) + (cn - cs) + (cf - cb);

	    sp(i,j,k) = w(i,j,k) * dxyz_dt - 
	      ( p(i,j,k+1)- p(i,j,k) ) * dxy
	      - (cep + cem - cwp - cwm + 
		 cnp + cnm - csp - csm +
		 cfp + cfm - cbp - cbm);    
	  }    
    calc_dw_3D();
    applyBoundaryConditions3D();
    return 0;     
}


} // Tuna namespace














